Families of Representational Failure: When Abstraction Loses Its Operational Guarantee

Systems fail in representational ways: something that is supposed to stand for an operational state does not carry the causal property required for that claim. This note identifies three structurally distinct families within this class of failure — representational substitution, representational incompleteness, and representational non-independence — and argues that these families differ not only in description but in the class of intervention required to address them. The key operational consequence: interventions that close failures of one family do not transfer to failures of another, and may reproduce the failure at a new layer.